We investigate the kinetics of phase separation in systems with a strong as
ymmetry in the mobility. This simple model system mimics the segregation ki
netics of polymer-solvent mixtures, where the polymer-rich phase forms a lo
w-mobility gel. We obtain detailed numerical results for this model, both w
ithout and with thermal noise. In the absence of thermal noise, we find tha
t domain growth is slowed down drastically when the low-mobility phase perc
olates the system. However, thermal noise restores rapid domain growth thro
ugh a Brownian coalescence mechanism.